Estimation of Endogenous Volatility Models with Exponential Trends

Juan R. A. Bobenrieth, Eugenio S. A. Bobenrieth, Andrés F. Villegas and Brian D. Wright
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Juan R. A. Bobenrieth: Departamento of Matemática, Universidad del Bío-Bío, Concepción 4081112, Chile
Eugenio S. A. Bobenrieth: Department of Agricultural Economics, Pontificia Universidad Católica de Chile, Santiago 8970117, Chile
Andrés F. Villegas: Escuela de Agronomía, Facultad de Recursos Naturales y Medicina Veterinaria, Universidad Santo Tomás, Santiago 8320000, Chile
Brian D. Wright: Department of Agricultural and Resource Economics, University of California Berkeley, Berkeley, CA 94720-3310, USA

Mathematics, 2022, vol. 10, issue 15, 1-27

Abstract: Nonlinearities, exponential trends, and Euler equations are three key features of standard dynamic volatility models of speculation, economic growth, or macroeconomic fluctuations with occasionally binding constraints and endogenous state-dependent volatility. A natural way to estimate a model with all such three features could be to use the observed nonstationary data in a single step without preliminary linearization, log-linearization, or preliminary detrending. Adoption of this natural strategy confronts a serious challenge that has been neither articulated nor solved: a dichotomy in the empirical model implied by the Euler equation. This leads to a discontinuity in the regression in the limit, rendering the approaches employed in available proofs of consistency inapplicable. We characterize the problem and develop a novel method of proof of consistency and asymptotic normality. Our methodological contribution establishes a foundation for consistent estimation and hypothesis testing of nonstationary models without resorting to preliminary detrending, an a priori assumption that any trend is exactly zero, linearization, or other restrictions on the model.

Keywords: asymptotic normality; commodity prices; dichotomy; dynamic nonlinear models; least squares; exponential trend; least squares; strong consistency; trend; asymptotic normality; endogenous volatility (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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